Find the molecular formula of a compound that contains 43.64 g of phosphorus and 56.36 g of oxygen. The molar mass of the compound is 283.9 g/mol.
To find the molecular formula of the compound, we first need to calculate the number of moles of each element present in the compound.
1. Calculate the number of moles of phosphorus:
Phosphorus (P):
Mass of phosphorus = 43.64 g
Molar mass of phosphorus = 30.97 g/mol
Number of moles = Mass / Molar mass
Number of moles of phosphorus = 43.64 g / 30.97 g/mol ≈ 1.41 mol
2. Calculate the number of moles of oxygen:
Oxygen (O):
Mass of oxygen = 56.36 g
Molar mass of oxygen = 15.999 g/mol
Number of moles = Mass / Molar mass
Number of moles of oxygen = 56.36 g / 15.999 g/mol ≈ 3.52 mol
3. Determine the empirical formula of the compound using the mole ratio of the elements:
Divide the number of moles of each element by the smallest number of moles:
Phosphorus: 1.41 mol / 1.41 mol = 1
Oxygen: 3.52 mol / 1.41 mol ≈ 2.5
This gives us an empirical formula of P1O2.5. However, we know that the molecular formula of the compound has a molar mass of 283.9 g/mol. To find the molecular formula, we need to determine the scaling factor that will give us a molar mass of 283.9 g/mol.
4. Calculate the molar mass of the empirical formula P1O2.5:
Molar mass of P = 30.97 g/mol
Molar mass of O = 15.999 g/mol
Molar mass of empirical formula = (1 x 30.97) + (2.5 x 15.999) ≈ 30.97 + 39.9975 ≈ 70.9675 g/mol
5. Determine the scaling factor:
Scaling factor = Molecular formula molar mass / Empirical formula molar mass
Scaling factor = 283.9 g/mol / 70.9675 g/mol ≈ 3.998
6. Multiply the subscripts in the empirical formula by the scaling factor to get the molecular formula:
Molecular formula = P4O10
Therefore, the molecular formula of the compound containing 43.64 g of phosphorus and 56.36 g of oxygen with a molar mass of 283.9 g/mol is P4O10.